Problem: Express this quotient in scientific notation: ${\frac{2.560\times 10^{-5}} {4.0\times 10^{-2}}}$
Answer: Start by collecting like terms together. $= {\frac{2.560} {4.0}} \times{\frac{10^{-5}} {10^{-2}}}$ Then divide each term separately. When dividing exponents with the same base, subtract their powers. $= 0.64 \times 10^{-5\,-\,-2}$ $= 0.64 \times 10^{-3}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$ . In this case, we need to move the decimal one position to the right without changing the value of our answer. $ $ We can use the fact that $0.64$ is the same as $6.40 \div 10$ , or $6.40 \times 10^{-1}$ $ = {6.40 \times 10^{-1}} \times 10^{-3} $ $= 6.40\times 10^{-4}$